Influencing Opinions of Heterogeneous Populations over Finite Time Horizons

Abstract

In this work, we focus on strategies to influence the opinion dynamics of a well-connected society. We propose a generalization of the popular voter model. This variant of the voter model can capture a wide range of individuals including strong-willed individuals whose opinion evolution is independent of their neighbors as well as conformist/rebel individuals who tend to adopt the opinion of the majority/minority. Motivated by political campaigns which aim to influence opinion dynamics by the end of a fixed deadline, we focus on influencing strategies for finite time horizons. We characterize the nature of optimal influencing strategies as a function of the nature of individuals forming the society. Using this, we show that for a society consisting of predominantly strongwilled/rebel individuals, the optimal strategy is to influence towards the end of the finite time horizon, whereas, for a society predominantly consisting of conformist individuals who try to adopt the opinion of the majority, it could be optimal to influence in the initial phase of the finite time horizon.

Influencing Opinion Dynamics in Networks with Limited Interaction

“…In this work, we consider two modes of opinion evolution, namely, organic evolution like in the voter model due to interactions with peers, and evolution due to external influence which attempts to move the network towards the favored opinion. Closest to our work, Kumar et al (2018) and Saxena et al (2020) also consider this hybrid ⋆ This work was supported in part by an Indo-French grant on Machine Learning for Network Analytics". The work of Neeraja Sahasrabudhe was also supported in part by the DST-INSPIRE Faculty Fellowship from the Govt.…”

“…A popular and widely studied binary opinion dynamics model is the voter model (Clifford and Sudbury (1973); Holley and Liggett (1975)). Many variants of the voter model have been proposed and studied, for instance, the linear threshold model proposed in Kempe et al (2003), the majority model proposed in Grtner and Zehmakan (2017), the conformist model and the strongwilled model studied in Kumar et al (2018), and the rebel model studied in Saxena et al (2020).…”

“…Given an influencing budget and a fixed time-horizon, the goal is to determine when to influence within the time-horizon to maximize the fraction of individuals with the preferred opinion at the end of the time-horizon. The key takeaway from Kumar et al (2018) and Saxena et al (2020) is that influencing at the beginning of the time horizon is more effective than influencing at the end only when individuals with a favorable opinion are less likely to change their opinion than individuals with an unfavorable opinion. In all other cases, the conventional wisdom of advertising towards the end of the time-horizon is indeed an optimal strategy.…”

“…In all other cases, the conventional wisdom of advertising towards the end of the time-horizon is indeed an optimal strategy. We generalize the setting studied in Kumar et al (2018) and Saxena et al (2020) by considering the case where, in each time-slot without external influence, the chosen individual changes their opinion with probability proportional to the fraction of individuals with the opposite opinion in a collection of opinions sought by the chosen individual. Unlike the setting in Kumar et al (2018) and Saxena et al (2020), this collection need not include the opinions of all the individuals in the network.…”

“…Our goal is to explore if the nature of optimal influencing strategies obtained in Kumar et al (2018) and Saxena et al (2020) are robust to these modifications. We focus on two specific ways through which this collection is curated.…”